Abstract
THE aim of this chapter is to give all the details of five other proofs (besides the one given in Chap. 3) of the Campbell, Baker, Hausdorff Theorem, stating that ; x♦y := Log(Exp(x) ·Exp(y)) is a series of Lie polynomials in x, y. As we showed in Chap. 3, this is the “qualitative” part of the CBHD Theorem, and the actual formula expressing xthat x♦y as an explicit series (that is, Dynkin’s Formula) can be quite easily derived from this qualitative counterpart as exhibited in Sect. 3.3.
Keywords
- Associative Algebra
- Formal Power Series
- Recursion Formula
- Bernoulli Number
- Topological Algebra
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© 2012 Springer-Verlag Berlin Heidelberg
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Bonfiglioli, A., Fulci, R. (2012). Some “Short” Proofs of the CBHD Theorem. In: Topics in Noncommutative Algebra. Lecture Notes in Mathematics(), vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22597-0_4
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DOI: https://doi.org/10.1007/978-3-642-22597-0_4
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